Shock waves will form by turning supersonic or locally supersonic flow and result in an increase in the freestream density downstream of the shock. This increase leads to optical distortions that limit the effectiveness of aircraft-mounted laser systems. In this paper, analytic expressions are developed to describe these optical distortions in terms of the optical-path difference (OPD). Pupil-plane disturbances imposed by the shock are studied for two cases: when the shock is parallel to the propagation direction and when the shock is on an angle relative to the propagation direction. Upon propagation from the pupil plane, the analysis shows that shock-induced phase discontinuities can sometimes cause the irradiance pattern in the image plane to bifurcate. Despite a large amount of tilt in the pupil plane, the bifurcated irradiance pattern does not map to a proportional shift in the image plane. The implications that these findings have on Shack–Hartmann wavefront sensor (SHWFS) data are also explored. The results show that least-squares reconstruction from the SHWFS data yield accurate estimates of the change in OPD across the shock when the magnitude of the phase difference [Formula: see text] caused by the shock is between 0 and approximately [Formula: see text]. However, when [Formula: see text], the results show that least-squares reconstruction begins to severely underestimate the change in OPD across the shock. Such results will inform future efforts looking to develop aircraft-mounted laser systems.
In this paper, atmospheric optical turbulence strength is estimated for realistic airborne environments using a modified phase-variance approach, as well as a modified slope-discrepancy approach. Realistic airborne environments are generated using wave-optics simulations of a plane wave propagating through increasing strengths of homogeneous atmospheric optical turbulence, both with and without aero-optical contamination (from in-flight wavefront sensor data) and additive-measurement noise. In comparison to the modified phase-variance approach, the results show that the modified slope-discrepancy approach more accurately estimates atmospheric optical turbulence strength over a wide range of conditions. Such results are encouraging for realistic airborne environments because they can be scaled to different freestream conditions as long as the boundary layer is considered canonical.
In this paper, an approach for detecting branch points using a Shack–Hartmann wavefront sensor (SHWFS) is introduced. Simulated data are created using Monte Carlo wave-optics simulations of varying turbulence strengths. It is assumed that the presence of a branch point in the SHWFS subaperture lenslet pupils causes appreciable beam spreading in the image plane. Therefore, second-moment statistics are used to quantify beam spread for each subaperture image-plane irradiance pattern. Thresholding is then employed to dictate what degree of beam spreading is sufficient to determine the presence of a branch point. Three different thresholds are imposed: liberal, moderate, and conservative. Furthermore, the collected SHWFS signal is treated as analog, digitized, and digitized with three levels of additive noise: low, moderate, and high. Monte Carlo simulations are conducted for 20 different spherical-wave Rytov numbers (RSW) ranging from 0.1 to 2.0. It was found that when conservative thresholds were employed, for the analog signal, digitized signal with no noise, and digitized signal with low noise, the percent of detections mostly comprised actual branch points, and false-positive detections were largely minimized. For the liberal thresholding cases, many false-positives were detected for all SHWFS signal types; however, significantly more branch points were also detected. The results presented in this paper are encouraging, and such results will inform efforts to develop branch-point tolerant least-squares reconstructors or use a SHWFS for optical-turbulence characterization in high-RSW environments.
Shock waves result from turning supersonic or locally supersonic flow and result in a large change in gas properties downstream of the shock. This change in gas properties, namely, the large increase in freestream density can affect the wavefront of a laser beam propagating through the shock. In this paper, analytic expressions are developed to describe the effects of these shock waves on the wavefront a laser beam propagating through the shock both parallel and on an angle relative to the shock direction. Furthermore, these near-field disturbances are then brought to a focus at the image-plane using a thin lens transmittance function with the Fresnel diffraction integral. The effects of the near-field disturbances imposed by the shock on the image-plane irradiance patterns are investigated and the implications of these image-plane irradiance patterns on Shack-Hartmann wavefront sensor measurements are also discussed.
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